Problem: Simplify the following expression: $\sqrt{208} + \sqrt{325}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{208} + \sqrt{325}$ $= \sqrt{16 \cdot 13} + \sqrt{25 \cdot 13}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{13} + \sqrt{25} \cdot \sqrt{13}$ $= 4\sqrt{13} + 5\sqrt{13}$ Finally, simplify by combining the terms. $= ( 4 + 5 )\sqrt{13} = 9\sqrt{13}$